They don't need to be approved in the typical FDA sense, but the ingredients do need to be considered GRAS (Generally Recognized as Safe).[1]
GRAS just tells people what they're allowed to sell, but most food products have been around long enough they are grandfathered in. The bigger issue that the FDA still mandates, is that the products are prepared under cGMP standards. The standards are open, available, and not at all onerous if you intend to be an honest business.[2]
Essentially, you need to have trained staff, clean buildings, batch records, clean equipment, known ingredients (no allergens accidentally introduced), etc. Really basic stuff. Unfortunately, it's mostly self-policed until an 'incident' at which case the FDA can do an audit and raise hell.
[1] - http://www.fda.gov/Food/IngredientsPackagingLabeling/GRAS/
[2] - http://www.fda.gov/cosmetics/guidancecomplianceregulatoryinf...